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Primel Metrology Wiki
(This wiki is under construction.) Welcome to the Primel Metrology Wiki The Primel Metrology is a new coherent dozenal-metric system of measurement based on certain fundamental realities of human life on Earth, including the mean solar day, the acceleration due Earth's gravity, the maximal density of water, the specific heat capacity of water, and other properties, with all units derived via 1:1 relationships without extraneous factors. Dozenal (base twelve) arithmetic Primel is a measurement system thoroughly grounded in duodecimal or "dozenal" base arithmetic. Given the high factorability of the number twelve compared to ten, dozenal is arguably a more convenient base for human use than decimal. It is for that very reason that so many historical systems of measure naturally incorporated factors of twelve. But what such systems lacked was a systematic design. Primel can be characterized as a "dozenal-metric" metrology, similar to the Tim-Grafut-Maz (TGM) metrology devised by Tom Pendlebury. Like TGM, Primel systematizes its units around powers of twelve to the same degree that the Metric system (now known as the International System of Units, or SI) systematizes its units around powers of ten. To avoid confusion, this wiki will use explicit base prefixes on all numbers: All numbers expressed in dozenal base will be prefixed with z|, all numbers expressed in decimal will be prefixed with d|. For instance, z|Ӿ = d|10, z|Ɛ = d|11, z|10 = d|12, z|100 = d|144, etc. Revised Systematic Dozenal Nomenclature (RSDN) RSDN provides a set of dozenal power prefixes (usable with any metrology) that are analogous to SI's decimal scaling prefixes. However, RSDN does not require an international committee to generate higher and higher order prefixes. Instead, it derives its prefixes systematically from a set of twelve familiar Greek and Latin numeric roots, each directly expressing the exponent in a power of twelve. These roots are identical to those used by the International Union of Pure and Applied Chemistry (IUPAC) to construct Systematic Element Names, with two additional roots, dec- and lev-, to represent ten and eleven as single digits in dozenal base (Ӿ and Ɛ). IUPAC chose its roots carefully so that they all begin with unique letters, making them amenable to single-character abbreviations. The dozenal additions maintain this uniqueness. RSDN also accommodates existing combination forms of these numeric roots, keeping intact their pre-existing meanings as simple multipliers. To avoid clashing with these forms, the power prefixes are derived by appending distinct syllables onto the roots: '-qua' for positive powers, '-cia' for negative powers. The following table lists the roots, the existing combination forms, and the corresponding power prefixes: When a multiplier contains multiple digits, or when the exponent of a power contains multiple digits, RSDN expresses these simply by concatenating the single-digit prefixes. This relies on exactly the same place-value arithmetic principle that Hindu-Arabic numerals employ. Hence, the next positive power above levqua-''' (z|10Ɛ), is '''unqua-'nilqua'- (z|1010), and the next negative power below levcia- (z|10-Ɛ) is uncia-'nilcia'- (z|10-10). Because the power prefixes are distinct from the existing multiplier forms, both can be freely combined without ambiguity, to create an analog of scientific notation: So for instance, bi-'hexa'-'penta'- represents z|265, bi-'hexa'-'pentqua'- represents z|26×105, bi-'hexqua'-'pentqua'- represents z|2×1065, and biqua-'hexqua'-'pentqua'- represents z|10265. Quantitels Quantitelsare systematic names for units of measure derived directly from the names of the physical quantities they measure, plus the ending -'el', which signifies "element", as in the familiar word "pixel" = "picture element". For example, lengthel is the quantitel for a unit of length. When a quantity has multiple synonyms (e.g. "work" and "energy"), it can have multiple synonymous quantitels (e.g. workel and energel); such synonyms can be used interchangeably. Quantitels are generic and can be used across potentially many metrologies. This particular metrology is named "Primel"' '''because it is the first (i.e., prime) system to use such unit names. "'Primel'" can be used as a disambiguating adjective to distinguish Primel quantitels from those of other metrologies (e.g. '''Primel lengthel'), but this is optional and may be omitted when the discussion is exclusively about Primel units. The prime character ( ′''' ) serves as an abbreviation for this prefix, marking every Primel unit as such (e.g. '''′lengthel). It may be left silent, or pronounced "prime" or "Primel" as needed. Colloquial Names In addition to systematic quantitel names, Primel proposes "colloquial" names, or "nicknames", for some of the base units, as well as for some useful multiples and dozenal powers of the base units. Some of these proposed nicknames will be purely fanciful. For instance, because the ′timel is rather short and fleeting, Primel proposes the colloquial name ′jiffy for this. But in many cases a nickname will be proposed because a unit closely approximates a customary or SI unit. For instance, because the ′lengthel approximates an archaic English length unit called the "barleycorn" (exactly 1/3 inch), Primel proposes the colloquial name ′kernel for this. Because the ′tri-lengthel approximates the customary inch (which in other languages is called a "thumb", e.g. Latin pollex), Primel proposes to nickname this the ′thumb. Because the ′unqua-lengthel approximates the customary "hand" measure, Primel proposes to nickname this the ′hand. 'Because the '′tri-unqua-lengthel approximates the customary foot, Primel proposes to nickname this the ′foot. And so forth. 1:1 Coherence Primel endeavors, where feasible, to relate the base units for different physical quantites using simple 1:1 ratios, without extraneous factors. (TGM also adheres to this principle.) Primel starts deriving its units by considering time first. The Day Primel uses a pure dozenal fraction of the mean solar day, namely the hexciaday (z|10-6 day), as the base unit of time (the ′timel), equivalent to d|50/1728 (z|0.042) seconds (nickname: ′jiffy). (This differs from TGM, which starts with a pure dozenal fraction of the hour instead.) Because of 1:1 coherence, this choice affects the sizes of all other base units in the metrology. It turns out that this yields many conveniently-sized units, either in the base units themselves, or when scaled using simple whole number multiples and/or pure dozenal powers (in the form of RSDN prefixes). Earth's Gravity For its unit of acceleration, the ′accelerel, Primel uses the net gravitational acceleration experienced on Earth's surface at the median latitude of d|45° (z|16%⊙). This is approximately d|9.80619920 m/s2. The SI standard gravity, d|9.80665 m/s2, was a late 19th century estimate of this median gravity that was unfortunately inaccurate compare to today's measurements. Today it is simply an arbitrary standard codified by SI. Primel opts for the more accurate modern value. From this unit of acceleration, Primel derives its units of velocity and length, following the principle of 1:1 coherence. The ′velocitel is the velocity a body achieves after falling for 1 ′timel under 1 ′accelerel of acceleration. This turns out to be remarkably close to 1 kilometer per hour (approximately d|1.0215 km/h), or 1 foot per second (approximately d|0.93 fps). The ′lengthel is the distance traversed by an object moving at a constant 1 ′velocitel for 1 ′timel. This turns out to be very close to 1/3 of an inch (about d|0.3232 in, or about d|8.21 mm), approximating the archaic English "barleycorn" measure, and hence giving this unit the nickname ′kernel. This results in a ′tri-'lengthel' (nickname: ′thumb) approximating an inch (about d|0.9697 inch, or about d|24.6 mm); an ′unqua-'lengthel' (nickname: ′hand) approximating both the customary 4-inch hand (about d|3.879 inch) and the SI decimeter (about d|98.5 mm); a ′tri-'unqua'-'lengthel' (nickname: ′foot) approximating the customary foot (about d|11.63 inch or d|0.295 m); and a ′biqua-'lengthel' (nickname ′ell) of about d|46.5 inch or d|1.18 m, approximating the d|45-inch English ell. From the ′lengthel in turn, Primel derives units of area, the ′areael (1 square ′lengthel), and volume, the ′volumel (1 cubic ′lengthel). The ′volumel is approximately d|0.55 ml. The ′triqua-'volumel' (nickname, ′handvol) comes remarkably close to a customary quart or an SI liter. (It is about 1.01 qt or d|0.956 L.) Density of Water Primel uses the maximal density of water as its base unit of density, the ′densitel. This leads to a unit of mass, the ′massel, of about d|0.55 grams (nickname: ′kernelmass); with the ′triqua-'massel' being just under 1 kilogram and just over 2 pounds (nickname: ′handmass). Because Earth's gravity is the unit of acceleration (1 ′accelerel = 1 ′accelerel), whatever the mass of anything is in ′massels, the force of its weight in ′forcels (or ′weightels) will be numerically the same (approximately, on Earth). So we could easily speak of the mass of something in ′kernelmasses or ′handmasses, and its weight in ′kernelweights or ′handweights, using (approximately) the same magnitudes. (Contrast this with the situation in SI, with kilograms of mass versus newtons of weight, with the factor of d|9.80665 m/s2 in between.) Units for energy, power, pressure, and the rest of Newtonian mechanics, are derived in straightforward fashion. Specific Thermal Capacity of Water To relate the phenomenon of heat and thermodynamics to the foundations of mechanics, Primel starts with a base unit for specific thermal capacity (the ′specithermacitel). This is set to a mean value for the specific thermal capacity of water. This leads to a unit for temperature (the ′temperaturel) defined as the increase in temperature induced in a 1 ′massel sample of water by applying 1 ′workel of heat energy. Since this turns out to be a very tiny amount of temperature, a dozenal power of this, the ′quadqua-'temperaturel', comes out to about d|0.4 kelvins, and thus is convenient for everyday use. This unit is nicknamed the ′stadigrade, because of the equivalence of heat energy to mechanical work: Raising the temperature of a body of water by one ′′′′ Primel provides three temperature scales based on the ′, but with different choices for a zero point: an Absolute scale zeroed at absolute zero, analogous to the Kelvin and Rankine scales; a Crystallic scale zeroed on the freezing point of water, somewhat resembling the Celsius scale; and a Familiar scale zeroed z|40 ′below freezing, bearing remarkable similarities to the Fahrenheit scale. Impedance of Free Space (TBD) Table of Primel Base Units The following table provides an executive summary of the Primel base units for each type of physical quantity. The names in the first column (will) serve as links to the wiki pages covering each type of physical quantity in more detail. Latest activity